Answer :

luisejr77

Answer: [tex]x=1.85[/tex]

Step-by-step explanation:

 Given the expression [tex]10^{4x-5}=e^{3x}[/tex], apply natural logarithm to both sides. Then:

[tex]ln(10)^{4x-5}=ln(e)^{3x}[/tex]

Remember that according the the properties of logarithms:

[tex]ln(a)^m=mln(a)[/tex]

[tex]ln(e)=1[/tex]

Then:

[tex](4x-5)ln(10)={3x}[/tex]

Apply distributive property and solve for "x". Then you get:

[tex]4x*ln(10)-5ln(10)=3x\\\\4x*ln(10)-3x=5ln(10)\\\\x(4ln(10)-3)=5ln(10)\\\\x=\frac{5ln(10)}{4ln(10)-3}\\\\x=1.85[/tex]

kudzordzifrancis

Answer:

[tex]x=1.85[/tex]

Step-by-step explanation:

The given exponential equation is;

[tex]10^{4x-5}=e^{3x}[/tex]

We take logarithm of both sides to base [tex]e[/tex].

[tex]\ln 10^{4x-5}=\ln e^{3x}[/tex]

[tex](4x-5)\ln 10=3x\ln e[/tex]

[tex](4x-5)\ln 10=3x[/tex]

Expand the left hand side;

[tex]4x\ln 10-5\ln 10=3x[/tex]

Group like terms

[tex]4x\ln 10-3x=5\ln 10[/tex]

[tex](4\ln 10-3)x=5\ln 10[/tex]

[tex]x=\frac{5\ln 10}{4\ln 10-3}[/tex]

[tex]x=1.85[/tex]

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